Problem: Solve for $x$ and $y$ using elimination. ${-6x+4y = 12}$ ${5x-3y = -7}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${-30x+20y = 60}$ $30x-18y = -42$ Add the top and bottom equations together. $2y = 18$ $\dfrac{2y}{{2}} = \dfrac{18}{{2}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-6x+4y = 12}\thinspace$ to find $x$ ${-6x + 4}{(9)}{= 12}$ $-6x+36 = 12$ $-6x+36{-36} = 12{-36}$ $-6x = -24$ $\dfrac{-6x}{{-6}} = \dfrac{-24}{{-6}}$ ${x = 4}$ You can also plug ${y = 9}$ into $\thinspace {5x-3y = -7}\thinspace$ and get the same answer for $x$ : ${5x - 3}{(9)}{= -7}$ ${x = 4}$